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A143214 Gray code applied to Pascal's triangle: T(n,k) = GrayCode(binomial(n, k)).

%I A143214 #21 Feb 16 2025 08:33:08
%S A143214 1,1,1,1,3,1,1,2,2,1,1,6,5,6,1,1,7,15,15,7,1,1,5,8,30,8,5,1,1,4,31,50,
%T A143214 50,31,4,1,1,12,18,36,101,36,18,12,1,1,13,54,126,65,65,126,54,13,1,1,
%U A143214 15,59,68,187,130,187,68,59,15,1
%N A143214 Gray code applied to Pascal's triangle: T(n,k) = GrayCode(binomial(n, k)).
%H A143214 G. C. Greubel, <a href="/A143214/b143214.txt">Rows n = 1..50 of the triangle, flattened</a>
%H A143214 Eric Weisstein, <a href="https://mathworld.wolfram.com/notebooks/Combinatorics/GrayCode.nb">Mathematica Notebook GrayCode.nb</a>
%H A143214 Eric Weisstein, <a href="https://mathworld.wolfram.com/GrayCode.html">Gray Code</a>, MathWorld.
%e A143214 Triangle begins as:
%e A143214   1;
%e A143214   1,  1;
%e A143214   1,  3,  1;
%e A143214   1,  2,  2,   1;
%e A143214   1,  6,  5,   6,   1;
%e A143214   1,  7, 15,  15,   7,   1;
%e A143214   1,  5,  8,  30,   8,   5,   1;
%e A143214   1,  4, 31,  50,  50,  31,   4,  1;
%e A143214   1, 12, 18,  36, 101,  36,  18, 12,  1;
%e A143214   1, 13, 54, 126,  65,  65, 126, 54, 13,  1;
%e A143214   1, 15, 59,  68, 187, 130, 187, 68, 59, 15, 1;
%t A143214 GrayCode[n_, k_]:= FromDigits[BitXor@@@Partition[Prepend[IntegerDigits[n, 2, k], 0], 2, 1], 2];
%t A143214 A143214[n_, k_]:= GrayCode[Binomial[n-1, k-1], 10];
%t A143214 Table[A143214[n,k], {n,12}, {k,n}]//Flatten
%Y A143214 Cf. A143213.
%K A143214 nonn,tabl
%O A143214 1,5
%A A143214 _Roger L. Bagula_ and _Gary W. Adamson_, Oct 20 2008
%E A143214 Edited by _Michel Marcus_ and _Joerg Arndt_, Apr 22 2013
%E A143214 Edited by _G. C. Greubel_, Aug 27 2024